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Italian MO 2017 P2

Source: Italian MO 2017 P2

May 6, 2017
algebranumber theory

Problem Statement

Let n≥2n\geq 2 be an integer. Consider the solutions of the system {n=a+b−cn=a2+b2−c2\begin{cases} n=a+b-c \\ n=a^2+b^2-c^2 \end{cases} where a,b,ca,b,c are integers. Show that there is at least one solution and that the solutions are finitely many.
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